Edge detection is an effective method for image segmentation and feature extraction. Therefore, extracting weak edges with the inhomogeneous gray of Corona Virus Disease 2019 (COVID-19) CT images is extremely important. Multiscale morphology has been widely used in the edge detection of medical images due to its excellent boundary detection accuracy. In this paper, we propose a weak edge detection method based on Gaussian filtering and singlescale Retinex (GF_SSR), and improved multiscale morphology and adaptive threshold binarization (IMSM_ATB). As all the CT images have noise, we propose to remove image noise by Gaussian filtering. The edge of CT images is enhanced using the SSR algorithm. In addition, based on the extracted edge of CT images using improved Multiscale morphology, a particle swarm optimization (PSO) algorithm is introduced to binarize the image by automatically getting the optimal threshold. To evaluate our method, we use images from three datasets, namely COVID-19, Kaggle-COVID-19, and COVID-Chestxray, respectively. The average values of results are worthy of reference, with the Shannon information entropy of 1.8539, the Precision of 0.9992, the Recall of 0.8224, the F-Score of 1.9158, running time of 11.3000. Finally, three types of lesion images in the COVID-19 dataset are selected to evaluate the visual effects of the proposed algorithm. Compared with the other four algorithms, the proposed algorithm effectively detects the weak edge of the lesion and provides help for image segmentation and feature extraction.